A fast two-stage algorithm for non-negative matrix factorization in smoothly varying data.

IF 1.9 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2023-03-01 DOI:10.1107/S2053273323000761

Ran Gu, Simon J L Billinge, Qiang Du

引用次数: 1

Abstract

This article reports the study of algorithms for non-negative matrix factorization (NMF) in various applications involving smoothly varying data such as time or temperature series diffraction data on a dense grid of points. Utilizing the continual nature of the data, a fast two-stage algorithm is developed for highly efficient and accurate NMF. In the first stage, an alternating non-negative least-squares framework is used in combination with the active set method with a warm-start strategy for the solution of subproblems. In the second stage, an interior point method is adopted to accelerate the local convergence. The convergence of the proposed algorithm is proved. The new algorithm is compared with some existing algorithms in benchmark tests using both real-world data and synthetic data. The results demonstrate the advantage of the algorithm in finding high-precision solutions.

Abstract Image

查看原文本刊更多论文

光滑变化数据中非负矩阵分解的快速两阶段算法。

本文研究了非负矩阵分解(NMF)算法在各种应用中的应用，这些应用涉及平滑变化的数据，如密集网格上的时间或温度序列衍射数据。利用数据的连续性，开发了一种快速的两阶段算法，用于高效准确的NMF。在第一阶段，采用交替非负最小二乘框架，结合具有热启动策略的活动集方法求解子问题。第二阶段采用内点法加快局部收敛速度。证明了该算法的收敛性。在实际数据和合成数据的基准测试中，将新算法与现有算法进行了比较。结果表明了该算法在求高精度解方面的优势。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Acta Crystallographica Section A: Foundations and Advances CHEMISTRY, MULTIDISCIPLINARYCRYSTALLOGRAPH-CRYSTALLOGRAPHY

CiteScore

2.60

自引率

11.10%

发文量

419

期刊介绍： Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials. The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial. The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.